numpy.random.RandomState.rayleigh¶
method

RandomState.
rayleigh
(scale=1.0, size=None)¶ Draw samples from a Rayleigh distribution.
The and Weibull distributions are generalizations of the Rayleigh.
Note
New code should use the
rayleigh
method of adefault_rng()
instance instead; see randomquickstart. Parameters
 scalefloat or array_like of floats, optional
Scale, also equals the mode. Must be nonnegative. Default is 1.
 sizeint or tuple of ints, optional
Output shape. If the given shape is, e.g.,
(m, n, k)
, thenm * n * k
samples are drawn. If size isNone
(default), a single value is returned ifscale
is a scalar. Otherwise,np.array(scale).size
samples are drawn.
 Returns
 outndarray or scalar
Drawn samples from the parameterized Rayleigh distribution.
See also
Generator.rayleigh
which should be used for new code.
Notes
The probability density function for the Rayleigh distribution is
The Rayleigh distribution would arise, for example, if the East and North components of the wind velocity had identical zeromean Gaussian distributions. Then the wind speed would have a Rayleigh distribution.
References
 1
Brighton Webs Ltd., “Rayleigh Distribution,” https://web.archive.org/web/20090514091424/http://brightonwebs.co.uk:80/distributions/rayleigh.asp
 2
Wikipedia, “Rayleigh distribution” https://en.wikipedia.org/wiki/Rayleigh_distribution
Examples
Draw values from the distribution and plot the histogram
>>> from matplotlib.pyplot import hist >>> values = hist(np.random.rayleigh(3, 100000), bins=200, density=True)
Wave heights tend to follow a Rayleigh distribution. If the mean wave height is 1 meter, what fraction of waves are likely to be larger than 3 meters?
>>> meanvalue = 1 >>> modevalue = np.sqrt(2 / np.pi) * meanvalue >>> s = np.random.rayleigh(modevalue, 1000000)
The percentage of waves larger than 3 meters is:
>>> 100.*sum(s>3)/1000000. 0.087300000000000003 # random